Holographic Thermodynamics and Information Conservation: Deriving the Cosmological Constant from Vacuum Entropy

ABSTRACT Contemporary physics has faced a persistent obstacle: the incompatibilitybetween the foundations of quantum mechanics and General Relativity. The clash of thesemodels generates a collection of theoretical anomalies, such as the miscalculation of thecosmological constant and the breakdown of unitarity at the event horizon of black holes.This work presents a new possibility to bypass this analytical collapse. Instead of insistingexclusively on the perturbative quantization of gravity and the uninterrupted search forundetectable mediating particles — such as the graviton —, I propose a restructuring ofpremises.This shift would require, first and foremost, reviewing the established conception ofspacetime itself. The model structured herein would demonstrate that the observableuniverse would function as a closed dissipative system, governed by a strict zero-summathematical balance. The cosmic mesh would lose the status of a passive geometricbackdrop to assume the function of an active mechanical operator, aimed at the selfoptimizationof the system. Traditional conservation laws would exit the stage, and the ruleof reactive thermodynamic compensation would take effect.The core of this formulation would be the Universal Equation of State. By modeling thebehavior of space through a closed path integral in proper time ( dτ ∮ = 0), it would becomeanalytically clear that the expansion of the universe would not be driven by obscure andrandom properties. The vector divergence of vacuum pressure would be rigorouslybalanced and annulled, moment by moment, by the rate at which the universe wouldproduce local informational entropy.From this premise, we would solve the mystery surrounding the missing energy in thecosmos. The cosmological constant — the much-debated Dark Energy — would cease tobe an anomaly in the density of the quantum vacuum and would pass to be understood asthe geometric thermodynamic cost exacted so that space could accommodate thecontinuous exhaustion of degrees of freedom generated by the collisions and interactionsof baryonic and non-baryonic matter.This same mechanics would naturally solve Hawking's information paradox. Under thisperspective, the black hole would depart from the definition of a destructive singularitytending toward infinity and would begin to act as a mere node of informational saturation atthe holographic bound. The quantum data that cross this horizon would not be erased;their integrity would remain preserved on the topological membrane and would becontinuously returned to the exterior in the form of perfectly correlated thermal radiation(Hawking Radiation).This framework would offer a solid mathematical basis to derive ab initio the couplingconstants of nature. Thus, we could review the structuring of research in high-energyphysics: laboratories and colliders could transition from classical mass spectrometry totrack anomalies of informational divergence, inaugurating the operational foundations for acosmology entirely based on the inviolable conservation of information and logical states. keywordsInformational Cosmology; Quantum Thermodynamics; Emergent Gravity; Universal Equationof State; Information Paradox; Dark Matter; CPT Symmetry.